Title: Estimating specification parameters while learning unknowns, in a misspecified model
Authors: Dalia Chakrabarty - Brunel University London (United Kingdom) [presenting]
Niharika Paul - University of Oxford (United Kingdom)
Abstract: A parametric relationship between an output and an input variable is often motivated, while arbitrarily assigning values to those model parameters that cannot be learnt/estimated using the available data. We refer to such parameters as Specification Parameters, SP, and these are typically parametrisations of symmetries in the behaviour/structure of systems, where said symmetries cannot be informed upon by available observations, though the assignment of incorrect values - in the data - to SPs, affects output prediction. Existing literature permits testing for misspecification of a model, but there is no suggestion on how to learn/estimate values of such SPs. We present a new method for optimising SPs, while learning the other unknown parameters of the model using MCMC-based inference, given the data. At each chosen value of the SP, we compute a new divergence measure, between results obtained from learning given the empirical data, and that given the generated data, where the latter data is sampled from the probability density function of the observable, given the learnable parameters that are learnt using the empirical data. Divergence minimisation yields optimal SP values. We will illustrate our method by estimating the observationally-elusive parametrisation of anisotropy of the phase space of a real galaxy (NGC4494), while learning the distribution of mass of the galactic gravitational matter, thus resolving lack of identifiability between galactic mass and anisotropy.